5G NR & LTE RAN Calculators

Architecture of 5G New Radio: Scalable Numerology and Flexible Frames

The architectural paradigm shift from 4G LTE to 5G New Radio (3GPP Releases 15 through 18) was anchored in the replacement of a rigid, static physical layer with a highly adaptable, software-reconfigurable framework. In 4G LTE, the air interface was strictly hardcoded to a 15 kHz subcarrier spacing (SCS), an invariable 1.0 ms subframe duration containing exactly two 0.5 ms slots (each containing 7 OFDM symbols under Normal Cyclic Prefix), and a uniform 100 kHz channel raster. While 15 kHz was well-matched to sub-3 GHz cellular propagation and mobile vehicular speeds, it imposed severe structural constraints when applied to wideband C-Band spectrum and ultra-high frequency millimeter-wave (FR2) regimes.

To transcend these limitations, 3GPP engineered the concept of scalable numerology (μ) in TS 38.211. Subcarrier spacing scales exponentially as an integer power of two:

Each numerology level μ halves the physical time-domain slot duration:

• μ = 0 (Δf = 15 kHz): Slot duration T_slot = 1.0 ms (14 symbols). Used predominantly in low-band FR1 spectrum (e.g., 600 MHz n71, 700 MHz n28, 850 MHz n5). Provides large symbol duration to mitigate extensive delay spread in multi-kilometer rural macrocells.
• μ = 1 (Δf = 30 kHz): Slot duration T_slot = 0.5 ms (14 symbols). The global benchmark workhorse for mid-band C-Band TDD deployments (n77, n78, n41). Offers optimal balance between delay spread tolerance, Phase Noise immunity, and low transmission latency.
• μ = 2 (Δf = 60 kHz): Slot duration T_slot = 0.25 ms (14 symbols). Supports both Normal and Extended Cyclic Prefix (ECP) for high-delay-spread dense deployments, as well as lower millimeter-wave FR2.
• μ = 3 (Δf = 120 kHz): Slot duration T_slot = 0.125 ms (14 symbols). Deployed across FR2 mmWave bands (n257, n258, n260, n261). The wide subcarrier spacing provides robust resilience against high Oscillator Phase Noise and high Doppler spreads common at 28 GHz and 39 GHz.

Crucially, regardless of numerology μ, a 3GPP Physical Resource Block (PRB) is invariably defined as exactly 12 consecutive subcarriers in the frequency domain. Consequently, a PRB occupies 180 kHz at μ=0, 360 kHz at μ=1, 720 kHz at μ=2, and 1.44 MHz at μ=3.

3GPP TS 38.214 Peak Throughput Formulation

Calculating peak theoretical user data rates across 5G New Radio networks is standardized in 3GPP TS 38.214 (Section 4.1.2). Rather than relying on empirical estimations, the standard articulates an exact physical layer summation across all aggregated component carriers:

Each mathematical parameter directly reflects a core air-interface layer constraint:

• MIMO Spatial Multiplexing Layers (v_Layers): Number of parallel spatial data streams (rank), ranging from 1 (SISO) up to 4 for standard UE receivers, and up to 8 layers for multi-user massive MIMO (MU-MIMO) beamformed transmissions.
• Modulation Order (Q_m): The number of bits transmitted per resource element symbol: QPSK (2), 16-QAM (4), 64-QAM (6), 256-QAM (8), and 1024-QAM (10).
• Scaling Factor / Duty Cycle (f): The effective downlink or uplink allocation ratio in time-domain TDD frames. In typical C-Band DDDSU slot configurations with 2.5 ms periodicity, f ≈ 0.7428. For balanced DSUUD patterns, f ≈ 0.40. In continuous FDD paired spectrum, f = 1.0.
• Maximum Code Rate (R_max): The maximum theoretical channel code rate achievable by 5G Low-Density Parity-Check (LDPC) coding schemes, specified as 948 / 1024 (≈ 0.92578125).
• Symbol Transmission Factor (12 / T_s^μ): The average OFDM symbol generation rate per second for one PRB. Since one slot contains 14 symbols and has duration 10⁻³ / (2^μ) seconds, the symbol rate evaluates to 12 × 14 × 2^μ × 1000 symbols/sec per PRB.
• Control Channel & Reference Overhead (OH): Accounts for Demodulation Reference Signals (DMRS), Channel State Information Reference Signals (CSI-RS), Synchronization Signal Blocks (SSB), and Physical Downlink Control Channel (PDCCH) symbols. 3GPP benchmarks OH at 0.14 for FR1 Downlink, 0.18 for FR2 Downlink, 0.08 for FR1 Uplink, and 0.10 for FR2 Uplink.

Carrier Aggregation (CA) and MIMO Scaling Mechanics

To achieve multi-gigabit throughput targets demanded by the ITU-R IMT-2020 specification, cellular operators leverage Carrier Aggregation (CA) and Massive MIMO spatial multiplexing. Carrier Aggregation aggregates up to 16 component carriers (CCs) across contiguous intra-band, non-contiguous intra-band, and inter-band spectrum combinations. For example, combining a 100 MHz TDD mid-band carrier (n78) with a 20 MHz FDD low-band anchor (n28) aggregates 120 MHz of instantaneous transmission bandwidth, allowing simultaneous high-rate payload streaming and resilient uplink control signaling via Supplementary Uplink (SUL).

Simultaneously, massive MIMO transceivers utilizing 32T32R or 64T64R active antenna units (AAUs) generate narrow, steerable pencil beams. Using Uplink-Downlink channel reciprocity in TDD through Sounding Reference Signals (SRS), the gNodeB computes precoding weight vectors that project orthogonal spatial streams to multiple user terminals on identical time-frequency resource elements, multiplying cell spectral efficiency by a factor of 3× to 5× over conventional sector antennas.

Timing Advance (TA) and Cell Ranging Physics

In high-speed cellular networks, orthogonal frequency division multiplexing requires all uplink transmissions from distributed user equipments (UEs) to arrive at the base station receiver antenna array within the cyclic prefix (CP) window. Because user equipments are located at varying propagation distances (ranging from tens of meters to dozens of kilometers from the gNodeB), signals transmitted at the same absolute instant would arrive staggered, destroying subcarrier orthogonality and causing severe inter-carrier interference (ICI).

To maintain strict time alignment, the gNodeB continuously issues Timing Advance (TA) commands via MAC Control Elements (MAC CE). The basic time unit of 5G NR is defined as:

Compared to LTE's legacy basic time unit T_s ≈ 32.552 ns, 5G NR's resolution is approximately 64 times finer. By measuring the round-trip propagation delay Δt, the physical distance between the user terminal and the cell tower can be computed with sub-meter theoretical precision via d = (c · Δt) / 2, where c is the speed of light in free space (299,792,458 m/s).

3GPP Standardized Bandwidth, Numerology & PRB Allocation Grid (TS 38.101-1 / TS 38.101-2)

The table below compiles 3GPP standardized transmission bandwidth configurations, allowable subcarrier spacings, maximum physical resource blocks (N_PRB), and benchmark downlink throughput under 4×4 MIMO and 256-QAM: